1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 140,084 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  2 111       2020-03-18 fema… 0-18  e380000… nhs_bed…    27 mk454hr  East of E…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_bla…     9 bb12fd   North West
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_bro…    11 br33ql   London    
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_can…     9 ws111jp  Midlands  
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_cit…    12 n15lz    London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_enf…     7 en40dy   London    
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_ham…     6 dl62uu   North Eas…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_har…    24 ts232la  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_kin…     6 kt11eu   London    
## # … with 140,074 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##     date_report               nhs_region deaths
## 1    2020-03-01          East of England      0
## 2    2020-03-02          East of England      1
## 3    2020-03-03          East of England      0
## 4    2020-03-04          East of England      0
## 5    2020-03-05          East of England      0
## 6    2020-03-06          East of England      1
## 7    2020-03-07          East of England      0
## 8    2020-03-08          East of England      0
## 9    2020-03-09          East of England      1
## 10   2020-03-10          East of England      0
## 11   2020-03-11          East of England      0
## 12   2020-03-12          East of England      0
## 13   2020-03-13          East of England      1
## 14   2020-03-14          East of England      2
## 15   2020-03-15          East of England      2
## 16   2020-03-16          East of England      1
## 17   2020-03-17          East of England      1
## 18   2020-03-18          East of England      5
## 19   2020-03-19          East of England      4
## 20   2020-03-20          East of England      2
## 21   2020-03-21          East of England     11
## 22   2020-03-22          East of England     12
## 23   2020-03-23          East of England     11
## 24   2020-03-24          East of England     19
## 25   2020-03-25          East of England     26
## 26   2020-03-26          East of England     36
## 27   2020-03-27          East of England     38
## 28   2020-03-28          East of England     28
## 29   2020-03-29          East of England     43
## 30   2020-03-30          East of England     45
## 31   2020-03-31          East of England     70
## 32   2020-04-01          East of England     61
## 33   2020-04-02          East of England     64
## 34   2020-04-03          East of England     80
## 35   2020-04-04          East of England     71
## 36   2020-04-05          East of England     76
## 37   2020-04-06          East of England     71
## 38   2020-04-07          East of England     93
## 39   2020-04-08          East of England    111
## 40   2020-04-09          East of England     87
## 41   2020-04-10          East of England     74
## 42   2020-04-11          East of England     91
## 43   2020-04-12          East of England    101
## 44   2020-04-13          East of England     78
## 45   2020-04-14          East of England     61
## 46   2020-04-15          East of England     82
## 47   2020-04-16          East of England     74
## 48   2020-04-17          East of England     86
## 49   2020-04-18          East of England     64
## 50   2020-04-19          East of England     67
## 51   2020-04-20          East of England     67
## 52   2020-04-21          East of England     75
## 53   2020-04-22          East of England     67
## 54   2020-04-23          East of England     49
## 55   2020-04-24          East of England     66
## 56   2020-04-25          East of England     54
## 57   2020-04-26          East of England     48
## 58   2020-04-27          East of England     46
## 59   2020-04-28          East of England     58
## 60   2020-04-29          East of England     32
## 61   2020-04-30          East of England     45
## 62   2020-05-01          East of England     49
## 63   2020-05-02          East of England     29
## 64   2020-05-03          East of England     41
## 65   2020-05-04          East of England     19
## 66   2020-05-05          East of England     36
## 67   2020-05-06          East of England     30
## 68   2020-05-07          East of England     33
## 69   2020-05-08          East of England     33
## 70   2020-05-09          East of England     29
## 71   2020-05-10          East of England     22
## 72   2020-05-11          East of England     18
## 73   2020-05-12          East of England     21
## 74   2020-05-13          East of England     27
## 75   2020-05-14          East of England     26
## 76   2020-05-15          East of England     19
## 77   2020-05-16          East of England     26
## 78   2020-05-17          East of England     17
## 79   2020-05-18          East of England     24
## 80   2020-05-19          East of England     15
## 81   2020-05-20          East of England     26
## 82   2020-05-21          East of England     21
## 83   2020-05-22          East of England     13
## 84   2020-05-23          East of England     12
## 85   2020-05-24          East of England     16
## 86   2020-05-25          East of England     25
## 87   2020-05-26          East of England     14
## 88   2020-05-27          East of England     12
## 89   2020-05-28          East of England     17
## 90   2020-05-29          East of England     15
## 91   2020-05-30          East of England      9
## 92   2020-05-31          East of England      8
## 93   2020-06-01          East of England     17
## 94   2020-06-02          East of England     14
## 95   2020-06-03          East of England      9
## 96   2020-06-04          East of England      6
## 97   2020-06-05          East of England     12
## 98   2020-06-06          East of England      4
## 99   2020-06-07          East of England      8
## 100  2020-06-08          East of England      4
## 101  2020-06-09          East of England      2
## 102  2020-03-01                   London      0
## 103  2020-03-02                   London      0
## 104  2020-03-03                   London      0
## 105  2020-03-04                   London      0
## 106  2020-03-05                   London      0
## 107  2020-03-06                   London      1
## 108  2020-03-07                   London      1
## 109  2020-03-08                   London      0
## 110  2020-03-09                   London      1
## 111  2020-03-10                   London      0
## 112  2020-03-11                   London      7
## 113  2020-03-12                   London      6
## 114  2020-03-13                   London     10
## 115  2020-03-14                   London     14
## 116  2020-03-15                   London     10
## 117  2020-03-16                   London     17
## 118  2020-03-17                   London     25
## 119  2020-03-18                   London     31
## 120  2020-03-19                   London     25
## 121  2020-03-20                   London     45
## 122  2020-03-21                   London     50
## 123  2020-03-22                   London     54
## 124  2020-03-23                   London     64
## 125  2020-03-24                   London     87
## 126  2020-03-25                   London    113
## 127  2020-03-26                   London    130
## 128  2020-03-27                   London    130
## 129  2020-03-28                   London    122
## 130  2020-03-29                   London    147
## 131  2020-03-30                   London    150
## 132  2020-03-31                   London    181
## 133  2020-04-01                   London    202
## 134  2020-04-02                   London    190
## 135  2020-04-03                   London    196
## 136  2020-04-04                   London    230
## 137  2020-04-05                   London    195
## 138  2020-04-06                   London    198
## 139  2020-04-07                   London    219
## 140  2020-04-08                   London    238
## 141  2020-04-09                   London    206
## 142  2020-04-10                   London    170
## 143  2020-04-11                   London    177
## 144  2020-04-12                   London    158
## 145  2020-04-13                   London    166
## 146  2020-04-14                   London    144
## 147  2020-04-15                   London    142
## 148  2020-04-16                   London    139
## 149  2020-04-17                   London    100
## 150  2020-04-18                   London    101
## 151  2020-04-19                   London    103
## 152  2020-04-20                   London     95
## 153  2020-04-21                   London     95
## 154  2020-04-22                   London    108
## 155  2020-04-23                   London     77
## 156  2020-04-24                   London     71
## 157  2020-04-25                   London     58
## 158  2020-04-26                   London     53
## 159  2020-04-27                   London     51
## 160  2020-04-28                   London     43
## 161  2020-04-29                   London     44
## 162  2020-04-30                   London     40
## 163  2020-05-01                   London     41
## 164  2020-05-02                   London     40
## 165  2020-05-03                   London     36
## 166  2020-05-04                   London     30
## 167  2020-05-05                   London     25
## 168  2020-05-06                   London     37
## 169  2020-05-07                   London     37
## 170  2020-05-08                   London     29
## 171  2020-05-09                   London     23
## 172  2020-05-10                   London     26
## 173  2020-05-11                   London     18
## 174  2020-05-12                   London     18
## 175  2020-05-13                   London     16
## 176  2020-05-14                   London     20
## 177  2020-05-15                   London     18
## 178  2020-05-16                   London     14
## 179  2020-05-17                   London     15
## 180  2020-05-18                   London      9
## 181  2020-05-19                   London     13
## 182  2020-05-20                   London     19
## 183  2020-05-21                   London     12
## 184  2020-05-22                   London     10
## 185  2020-05-23                   London      6
## 186  2020-05-24                   London      7
## 187  2020-05-25                   London      9
## 188  2020-05-26                   London     12
## 189  2020-05-27                   London      7
## 190  2020-05-28                   London      8
## 191  2020-05-29                   London      7
## 192  2020-05-30                   London     12
## 193  2020-05-31                   London      6
## 194  2020-06-01                   London      9
## 195  2020-06-02                   London      7
## 196  2020-06-03                   London      5
## 197  2020-06-04                   London      8
## 198  2020-06-05                   London      3
## 199  2020-06-06                   London      0
## 200  2020-06-07                   London      4
## 201  2020-06-08                   London      4
## 202  2020-06-09                   London      0
## 203  2020-03-01                 Midlands      0
## 204  2020-03-02                 Midlands      0
## 205  2020-03-03                 Midlands      1
## 206  2020-03-04                 Midlands      0
## 207  2020-03-05                 Midlands      0
## 208  2020-03-06                 Midlands      0
## 209  2020-03-07                 Midlands      0
## 210  2020-03-08                 Midlands      3
## 211  2020-03-09                 Midlands      1
## 212  2020-03-10                 Midlands      0
## 213  2020-03-11                 Midlands      2
## 214  2020-03-12                 Midlands      6
## 215  2020-03-13                 Midlands      5
## 216  2020-03-14                 Midlands      4
## 217  2020-03-15                 Midlands      5
## 218  2020-03-16                 Midlands     11
## 219  2020-03-17                 Midlands      8
## 220  2020-03-18                 Midlands     13
## 221  2020-03-19                 Midlands      8
## 222  2020-03-20                 Midlands     28
## 223  2020-03-21                 Midlands     13
## 224  2020-03-22                 Midlands     31
## 225  2020-03-23                 Midlands     33
## 226  2020-03-24                 Midlands     41
## 227  2020-03-25                 Midlands     48
## 228  2020-03-26                 Midlands     64
## 229  2020-03-27                 Midlands     72
## 230  2020-03-28                 Midlands     89
## 231  2020-03-29                 Midlands     92
## 232  2020-03-30                 Midlands     90
## 233  2020-03-31                 Midlands    123
## 234  2020-04-01                 Midlands    140
## 235  2020-04-02                 Midlands    142
## 236  2020-04-03                 Midlands    124
## 237  2020-04-04                 Midlands    151
## 238  2020-04-05                 Midlands    164
## 239  2020-04-06                 Midlands    140
## 240  2020-04-07                 Midlands    123
## 241  2020-04-08                 Midlands    186
## 242  2020-04-09                 Midlands    139
## 243  2020-04-10                 Midlands    127
## 244  2020-04-11                 Midlands    142
## 245  2020-04-12                 Midlands    139
## 246  2020-04-13                 Midlands    120
## 247  2020-04-14                 Midlands    116
## 248  2020-04-15                 Midlands    147
## 249  2020-04-16                 Midlands    102
## 250  2020-04-17                 Midlands    118
## 251  2020-04-18                 Midlands    115
## 252  2020-04-19                 Midlands     92
## 253  2020-04-20                 Midlands    107
## 254  2020-04-21                 Midlands     86
## 255  2020-04-22                 Midlands     78
## 256  2020-04-23                 Midlands    103
## 257  2020-04-24                 Midlands     79
## 258  2020-04-25                 Midlands     72
## 259  2020-04-26                 Midlands     81
## 260  2020-04-27                 Midlands     74
## 261  2020-04-28                 Midlands     68
## 262  2020-04-29                 Midlands     53
## 263  2020-04-30                 Midlands     56
## 264  2020-05-01                 Midlands     64
## 265  2020-05-02                 Midlands     51
## 266  2020-05-03                 Midlands     52
## 267  2020-05-04                 Midlands     61
## 268  2020-05-05                 Midlands     58
## 269  2020-05-06                 Midlands     59
## 270  2020-05-07                 Midlands     48
## 271  2020-05-08                 Midlands     34
## 272  2020-05-09                 Midlands     37
## 273  2020-05-10                 Midlands     42
## 274  2020-05-11                 Midlands     33
## 275  2020-05-12                 Midlands     45
## 276  2020-05-13                 Midlands     39
## 277  2020-05-14                 Midlands     37
## 278  2020-05-15                 Midlands     40
## 279  2020-05-16                 Midlands     34
## 280  2020-05-17                 Midlands     31
## 281  2020-05-18                 Midlands     34
## 282  2020-05-19                 Midlands     34
## 283  2020-05-20                 Midlands     36
## 284  2020-05-21                 Midlands     32
## 285  2020-05-22                 Midlands     27
## 286  2020-05-23                 Midlands     34
## 287  2020-05-24                 Midlands     19
## 288  2020-05-25                 Midlands     26
## 289  2020-05-26                 Midlands     33
## 290  2020-05-27                 Midlands     29
## 291  2020-05-28                 Midlands     27
## 292  2020-05-29                 Midlands     20
## 293  2020-05-30                 Midlands     20
## 294  2020-05-31                 Midlands     20
## 295  2020-06-01                 Midlands     20
## 296  2020-06-02                 Midlands     20
## 297  2020-06-03                 Midlands     23
## 298  2020-06-04                 Midlands     14
## 299  2020-06-05                 Midlands     21
## 300  2020-06-06                 Midlands     18
## 301  2020-06-07                 Midlands     13
## 302  2020-06-08                 Midlands     10
## 303  2020-06-09                 Midlands      0
## 304  2020-03-01 North East and Yorkshire      0
## 305  2020-03-02 North East and Yorkshire      0
## 306  2020-03-03 North East and Yorkshire      0
## 307  2020-03-04 North East and Yorkshire      0
## 308  2020-03-05 North East and Yorkshire      0
## 309  2020-03-06 North East and Yorkshire      0
## 310  2020-03-07 North East and Yorkshire      0
## 311  2020-03-08 North East and Yorkshire      0
## 312  2020-03-09 North East and Yorkshire      0
## 313  2020-03-10 North East and Yorkshire      0
## 314  2020-03-11 North East and Yorkshire      0
## 315  2020-03-12 North East and Yorkshire      0
## 316  2020-03-13 North East and Yorkshire      0
## 317  2020-03-14 North East and Yorkshire      0
## 318  2020-03-15 North East and Yorkshire      2
## 319  2020-03-16 North East and Yorkshire      3
## 320  2020-03-17 North East and Yorkshire      1
## 321  2020-03-18 North East and Yorkshire      2
## 322  2020-03-19 North East and Yorkshire      6
## 323  2020-03-20 North East and Yorkshire      5
## 324  2020-03-21 North East and Yorkshire      6
## 325  2020-03-22 North East and Yorkshire      7
## 326  2020-03-23 North East and Yorkshire      9
## 327  2020-03-24 North East and Yorkshire      8
## 328  2020-03-25 North East and Yorkshire     18
## 329  2020-03-26 North East and Yorkshire     21
## 330  2020-03-27 North East and Yorkshire     28
## 331  2020-03-28 North East and Yorkshire     35
## 332  2020-03-29 North East and Yorkshire     38
## 333  2020-03-30 North East and Yorkshire     64
## 334  2020-03-31 North East and Yorkshire     60
## 335  2020-04-01 North East and Yorkshire     67
## 336  2020-04-02 North East and Yorkshire     74
## 337  2020-04-03 North East and Yorkshire    100
## 338  2020-04-04 North East and Yorkshire    105
## 339  2020-04-05 North East and Yorkshire     92
## 340  2020-04-06 North East and Yorkshire     96
## 341  2020-04-07 North East and Yorkshire    102
## 342  2020-04-08 North East and Yorkshire    107
## 343  2020-04-09 North East and Yorkshire    111
## 344  2020-04-10 North East and Yorkshire    117
## 345  2020-04-11 North East and Yorkshire     98
## 346  2020-04-12 North East and Yorkshire     84
## 347  2020-04-13 North East and Yorkshire     94
## 348  2020-04-14 North East and Yorkshire    107
## 349  2020-04-15 North East and Yorkshire     96
## 350  2020-04-16 North East and Yorkshire    103
## 351  2020-04-17 North East and Yorkshire     88
## 352  2020-04-18 North East and Yorkshire     95
## 353  2020-04-19 North East and Yorkshire     88
## 354  2020-04-20 North East and Yorkshire    100
## 355  2020-04-21 North East and Yorkshire     76
## 356  2020-04-22 North East and Yorkshire     84
## 357  2020-04-23 North East and Yorkshire     63
## 358  2020-04-24 North East and Yorkshire     72
## 359  2020-04-25 North East and Yorkshire     69
## 360  2020-04-26 North East and Yorkshire     65
## 361  2020-04-27 North East and Yorkshire     65
## 362  2020-04-28 North East and Yorkshire     57
## 363  2020-04-29 North East and Yorkshire     69
## 364  2020-04-30 North East and Yorkshire     57
## 365  2020-05-01 North East and Yorkshire     64
## 366  2020-05-02 North East and Yorkshire     48
## 367  2020-05-03 North East and Yorkshire     40
## 368  2020-05-04 North East and Yorkshire     49
## 369  2020-05-05 North East and Yorkshire     40
## 370  2020-05-06 North East and Yorkshire     50
## 371  2020-05-07 North East and Yorkshire     45
## 372  2020-05-08 North East and Yorkshire     42
## 373  2020-05-09 North East and Yorkshire     44
## 374  2020-05-10 North East and Yorkshire     40
## 375  2020-05-11 North East and Yorkshire     29
## 376  2020-05-12 North East and Yorkshire     27
## 377  2020-05-13 North East and Yorkshire     28
## 378  2020-05-14 North East and Yorkshire     30
## 379  2020-05-15 North East and Yorkshire     32
## 380  2020-05-16 North East and Yorkshire     35
## 381  2020-05-17 North East and Yorkshire     26
## 382  2020-05-18 North East and Yorkshire     29
## 383  2020-05-19 North East and Yorkshire     27
## 384  2020-05-20 North East and Yorkshire     21
## 385  2020-05-21 North East and Yorkshire     33
## 386  2020-05-22 North East and Yorkshire     22
## 387  2020-05-23 North East and Yorkshire     18
## 388  2020-05-24 North East and Yorkshire     24
## 389  2020-05-25 North East and Yorkshire     21
## 390  2020-05-26 North East and Yorkshire     21
## 391  2020-05-27 North East and Yorkshire     21
## 392  2020-05-28 North East and Yorkshire     19
## 393  2020-05-29 North East and Yorkshire     24
## 394  2020-05-30 North East and Yorkshire     20
## 395  2020-05-31 North East and Yorkshire     18
## 396  2020-06-01 North East and Yorkshire     16
## 397  2020-06-02 North East and Yorkshire     22
## 398  2020-06-03 North East and Yorkshire     21
## 399  2020-06-04 North East and Yorkshire     17
## 400  2020-06-05 North East and Yorkshire     16
## 401  2020-06-06 North East and Yorkshire     20
## 402  2020-06-07 North East and Yorkshire     11
## 403  2020-06-08 North East and Yorkshire     10
## 404  2020-06-09 North East and Yorkshire      5
## 405  2020-03-01               North West      0
## 406  2020-03-02               North West      0
## 407  2020-03-03               North West      0
## 408  2020-03-04               North West      0
## 409  2020-03-05               North West      1
## 410  2020-03-06               North West      0
## 411  2020-03-07               North West      0
## 412  2020-03-08               North West      1
## 413  2020-03-09               North West      0
## 414  2020-03-10               North West      0
## 415  2020-03-11               North West      0
## 416  2020-03-12               North West      2
## 417  2020-03-13               North West      3
## 418  2020-03-14               North West      1
## 419  2020-03-15               North West      4
## 420  2020-03-16               North West      2
## 421  2020-03-17               North West      4
## 422  2020-03-18               North West      6
## 423  2020-03-19               North West      7
## 424  2020-03-20               North West     10
## 425  2020-03-21               North West     11
## 426  2020-03-22               North West     13
## 427  2020-03-23               North West     16
## 428  2020-03-24               North West     21
## 429  2020-03-25               North West     21
## 430  2020-03-26               North West     29
## 431  2020-03-27               North West     35
## 432  2020-03-28               North West     28
## 433  2020-03-29               North West     46
## 434  2020-03-30               North West     67
## 435  2020-03-31               North West     52
## 436  2020-04-01               North West     86
## 437  2020-04-02               North West     96
## 438  2020-04-03               North West     95
## 439  2020-04-04               North West     98
## 440  2020-04-05               North West    102
## 441  2020-04-06               North West    100
## 442  2020-04-07               North West    134
## 443  2020-04-08               North West    127
## 444  2020-04-09               North West    119
## 445  2020-04-10               North West    117
## 446  2020-04-11               North West    138
## 447  2020-04-12               North West    126
## 448  2020-04-13               North West    129
## 449  2020-04-14               North West    131
## 450  2020-04-15               North West    114
## 451  2020-04-16               North West    134
## 452  2020-04-17               North West     98
## 453  2020-04-18               North West    113
## 454  2020-04-19               North West     71
## 455  2020-04-20               North West     83
## 456  2020-04-21               North West     76
## 457  2020-04-22               North West     86
## 458  2020-04-23               North West     85
## 459  2020-04-24               North West     66
## 460  2020-04-25               North West     65
## 461  2020-04-26               North West     55
## 462  2020-04-27               North West     54
## 463  2020-04-28               North West     57
## 464  2020-04-29               North West     62
## 465  2020-04-30               North West     59
## 466  2020-05-01               North West     44
## 467  2020-05-02               North West     56
## 468  2020-05-03               North West     55
## 469  2020-05-04               North West     48
## 470  2020-05-05               North West     48
## 471  2020-05-06               North West     44
## 472  2020-05-07               North West     49
## 473  2020-05-08               North West     42
## 474  2020-05-09               North West     30
## 475  2020-05-10               North West     41
## 476  2020-05-11               North West     34
## 477  2020-05-12               North West     38
## 478  2020-05-13               North West     24
## 479  2020-05-14               North West     26
## 480  2020-05-15               North West     33
## 481  2020-05-16               North West     32
## 482  2020-05-17               North West     24
## 483  2020-05-18               North West     31
## 484  2020-05-19               North West     35
## 485  2020-05-20               North West     27
## 486  2020-05-21               North West     26
## 487  2020-05-22               North West     26
## 488  2020-05-23               North West     31
## 489  2020-05-24               North West     26
## 490  2020-05-25               North West     31
## 491  2020-05-26               North West     27
## 492  2020-05-27               North West     27
## 493  2020-05-28               North West     28
## 494  2020-05-29               North West     19
## 495  2020-05-30               North West     17
## 496  2020-05-31               North West     13
## 497  2020-06-01               North West     12
## 498  2020-06-02               North West     26
## 499  2020-06-03               North West     21
## 500  2020-06-04               North West     19
## 501  2020-06-05               North West     15
## 502  2020-06-06               North West     18
## 503  2020-06-07               North West     15
## 504  2020-06-08               North West     16
## 505  2020-06-09               North West      2
## 506  2020-03-01               South East      0
## 507  2020-03-02               South East      0
## 508  2020-03-03               South East      1
## 509  2020-03-04               South East      0
## 510  2020-03-05               South East      1
## 511  2020-03-06               South East      0
## 512  2020-03-07               South East      0
## 513  2020-03-08               South East      1
## 514  2020-03-09               South East      1
## 515  2020-03-10               South East      1
## 516  2020-03-11               South East      1
## 517  2020-03-12               South East      0
## 518  2020-03-13               South East      1
## 519  2020-03-14               South East      1
## 520  2020-03-15               South East      5
## 521  2020-03-16               South East      8
## 522  2020-03-17               South East      7
## 523  2020-03-18               South East     10
## 524  2020-03-19               South East      9
## 525  2020-03-20               South East     14
## 526  2020-03-21               South East      7
## 527  2020-03-22               South East     25
## 528  2020-03-23               South East     20
## 529  2020-03-24               South East     22
## 530  2020-03-25               South East     29
## 531  2020-03-26               South East     34
## 532  2020-03-27               South East     34
## 533  2020-03-28               South East     36
## 534  2020-03-29               South East     54
## 535  2020-03-30               South East     58
## 536  2020-03-31               South East     65
## 537  2020-04-01               South East     65
## 538  2020-04-02               South East     55
## 539  2020-04-03               South East     72
## 540  2020-04-04               South East     80
## 541  2020-04-05               South East     82
## 542  2020-04-06               South East     88
## 543  2020-04-07               South East    100
## 544  2020-04-08               South East     83
## 545  2020-04-09               South East    104
## 546  2020-04-10               South East     88
## 547  2020-04-11               South East     88
## 548  2020-04-12               South East     88
## 549  2020-04-13               South East     84
## 550  2020-04-14               South East     65
## 551  2020-04-15               South East     72
## 552  2020-04-16               South East     56
## 553  2020-04-17               South East     86
## 554  2020-04-18               South East     57
## 555  2020-04-19               South East     70
## 556  2020-04-20               South East     85
## 557  2020-04-21               South East     50
## 558  2020-04-22               South East     54
## 559  2020-04-23               South East     57
## 560  2020-04-24               South East     64
## 561  2020-04-25               South East     51
## 562  2020-04-26               South East     51
## 563  2020-04-27               South East     40
## 564  2020-04-28               South East     40
## 565  2020-04-29               South East     47
## 566  2020-04-30               South East     29
## 567  2020-05-01               South East     37
## 568  2020-05-02               South East     36
## 569  2020-05-03               South East     17
## 570  2020-05-04               South East     35
## 571  2020-05-05               South East     29
## 572  2020-05-06               South East     25
## 573  2020-05-07               South East     27
## 574  2020-05-08               South East     26
## 575  2020-05-09               South East     28
## 576  2020-05-10               South East     19
## 577  2020-05-11               South East     25
## 578  2020-05-12               South East     27
## 579  2020-05-13               South East     18
## 580  2020-05-14               South East     32
## 581  2020-05-15               South East     24
## 582  2020-05-16               South East     22
## 583  2020-05-17               South East     18
## 584  2020-05-18               South East     22
## 585  2020-05-19               South East     12
## 586  2020-05-20               South East     22
## 587  2020-05-21               South East     14
## 588  2020-05-22               South East     17
## 589  2020-05-23               South East     21
## 590  2020-05-24               South East     16
## 591  2020-05-25               South East     13
## 592  2020-05-26               South East     19
## 593  2020-05-27               South East     17
## 594  2020-05-28               South East     12
## 595  2020-05-29               South East     17
## 596  2020-05-30               South East      8
## 597  2020-05-31               South East     10
## 598  2020-06-01               South East     11
## 599  2020-06-02               South East     11
## 600  2020-06-03               South East     17
## 601  2020-06-04               South East      9
## 602  2020-06-05               South East      9
## 603  2020-06-06               South East      6
## 604  2020-06-07               South East      7
## 605  2020-06-08               South East      4
## 606  2020-06-09               South East      2
## 607  2020-03-01               South West      0
## 608  2020-03-02               South West      0
## 609  2020-03-03               South West      0
## 610  2020-03-04               South West      0
## 611  2020-03-05               South West      0
## 612  2020-03-06               South West      0
## 613  2020-03-07               South West      0
## 614  2020-03-08               South West      0
## 615  2020-03-09               South West      0
## 616  2020-03-10               South West      0
## 617  2020-03-11               South West      1
## 618  2020-03-12               South West      0
## 619  2020-03-13               South West      0
## 620  2020-03-14               South West      1
## 621  2020-03-15               South West      0
## 622  2020-03-16               South West      0
## 623  2020-03-17               South West      2
## 624  2020-03-18               South West      2
## 625  2020-03-19               South West      5
## 626  2020-03-20               South West      3
## 627  2020-03-21               South West      6
## 628  2020-03-22               South West      9
## 629  2020-03-23               South West      9
## 630  2020-03-24               South West      7
## 631  2020-03-25               South West      9
## 632  2020-03-26               South West     11
## 633  2020-03-27               South West     13
## 634  2020-03-28               South West     21
## 635  2020-03-29               South West     18
## 636  2020-03-30               South West     23
## 637  2020-03-31               South West     23
## 638  2020-04-01               South West     22
## 639  2020-04-02               South West     23
## 640  2020-04-03               South West     30
## 641  2020-04-04               South West     42
## 642  2020-04-05               South West     32
## 643  2020-04-06               South West     34
## 644  2020-04-07               South West     39
## 645  2020-04-08               South West     47
## 646  2020-04-09               South West     24
## 647  2020-04-10               South West     46
## 648  2020-04-11               South West     43
## 649  2020-04-12               South West     23
## 650  2020-04-13               South West     27
## 651  2020-04-14               South West     24
## 652  2020-04-15               South West     32
## 653  2020-04-16               South West     29
## 654  2020-04-17               South West     33
## 655  2020-04-18               South West     25
## 656  2020-04-19               South West     31
## 657  2020-04-20               South West     26
## 658  2020-04-21               South West     26
## 659  2020-04-22               South West     22
## 660  2020-04-23               South West     17
## 661  2020-04-24               South West     19
## 662  2020-04-25               South West     15
## 663  2020-04-26               South West     27
## 664  2020-04-27               South West     13
## 665  2020-04-28               South West     17
## 666  2020-04-29               South West     15
## 667  2020-04-30               South West     26
## 668  2020-05-01               South West      6
## 669  2020-05-02               South West      7
## 670  2020-05-03               South West     10
## 671  2020-05-04               South West     16
## 672  2020-05-05               South West     14
## 673  2020-05-06               South West     19
## 674  2020-05-07               South West     16
## 675  2020-05-08               South West      6
## 676  2020-05-09               South West     11
## 677  2020-05-10               South West      5
## 678  2020-05-11               South West      8
## 679  2020-05-12               South West      7
## 680  2020-05-13               South West      7
## 681  2020-05-14               South West      6
## 682  2020-05-15               South West      4
## 683  2020-05-16               South West      4
## 684  2020-05-17               South West      6
## 685  2020-05-18               South West      4
## 686  2020-05-19               South West      6
## 687  2020-05-20               South West      1
## 688  2020-05-21               South West      9
## 689  2020-05-22               South West      6
## 690  2020-05-23               South West      6
## 691  2020-05-24               South West      3
## 692  2020-05-25               South West      8
## 693  2020-05-26               South West     11
## 694  2020-05-27               South West      5
## 695  2020-05-28               South West      9
## 696  2020-05-29               South West      4
## 697  2020-05-30               South West      3
## 698  2020-05-31               South West      2
## 699  2020-06-01               South West      6
## 700  2020-06-02               South West      2
## 701  2020-06-03               South West      5
## 702  2020-06-04               South West      1
## 703  2020-06-05               South West      1
## 704  2020-06-06               South West      1
## 705  2020-06-07               South West      2
## 706  2020-06-08               South West      2
## 707  2020-06-09               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-06-09"

The completion date of the NHS Pathways data is Tuesday 09 Jun 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -8.1172  -2.0912  -0.2046   1.9561   4.5140  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 5.079e+00  5.087e-02   99.85   <2e-16 ***
## note_lag    1.056e-05  4.922e-07   21.45   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 8.02555)
## 
##     Null deviance: 4005.2  on 39  degrees of freedom
## Residual deviance:  313.4  on 38  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  160.684073    1.000011
exp(confint(lag_mod))
##                 2.5 %     97.5 %
## (Intercept) 145.29180 177.359896
## note_lag      1.00001   1.000012

Rsq(lag_mod)
## [1] 0.9217528

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.5.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.5.0: Tue May 26 20:41:44 PDT 2020; root:xnu-6153.121.2~2/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                   "Mac-1467.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin15.6.0   
## arch           x86_64                      
## os             darwin15.6.0                
## system         x86_64, darwin15.6.0        
## status                                     
## major          3                           
## minor          6.3                         
## year           2020                        
## month          02                          
## day            29                          
## svn rev        77875                       
## language       R                           
## version.string R version 3.6.3 (2020-02-29)
## nickname       Holding the Windsock

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Catalina 10.15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.3.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.13             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.1.1       
## [10] projections_0.4.1    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.1      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.5          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.1         ggplot2_3.3.1       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] colorspace_1.4-1  selectr_0.4-2     ggsignif_0.6.0    ellipsis_0.3.1   
##  [5] rprojroot_1.3-2   snakecase_0.11.0  fs_1.4.1          rstudioapi_0.11  
##  [9] farver_2.0.3      fansi_0.4.1       splines_3.6.3     knitr_1.28       
## [13] jsonlite_1.6.1    broom_0.5.6       dbplyr_1.4.4      compiler_3.6.3   
## [17] httr_1.4.1        backports_1.1.7   assertthat_0.2.1  Matrix_1.2-18    
## [21] cli_2.0.2         htmltools_0.4.0   prettyunits_1.1.1 tools_3.6.3      
## [25] gtable_0.3.0      glue_1.4.1        Rcpp_1.0.4.6      carData_3.0-4    
## [29] cellranger_1.1.0  vctrs_0.3.1       nlme_3.1-144      matchmaker_0.1.1 
## [33] crosstalk_1.1.0.1 xfun_0.14         ps_1.3.3          openxlsx_4.1.5   
## [37] lifecycle_0.2.0   rstatix_0.5.0     MASS_7.3-51.5     scales_1.1.1     
## [41] hms_0.5.3         sodium_1.1        yaml_2.2.1        curl_4.3         
## [45] gridExtra_2.3     stringi_1.4.6     kyotil_2019.11-22 boot_1.3-24      
## [49] pkgbuild_1.0.8    zip_2.0.4         rlang_0.4.6       pkgconfig_2.0.3  
## [53] evaluate_0.14     lattice_0.20-38   labeling_0.3      htmlwidgets_1.5.1
## [57] cowplot_1.0.0     processx_3.4.2    tidyselect_1.1.0  plyr_1.8.6       
## [61] magrittr_1.5      R6_2.4.1          generics_0.0.2    DBI_1.1.0        
## [65] pillar_1.4.4      haven_2.3.1       foreign_0.8-75    withr_2.2.0      
## [69] mgcv_1.8-31       survival_3.1-8    abind_1.4-5       modelr_0.1.8     
## [73] crayon_1.3.4      car_3.0-8         utf8_1.1.4        rmarkdown_2.2    
## [77] viridis_0.5.1     grid_3.6.3        readxl_1.3.1      data.table_1.12.8
## [81] blob_1.2.1        callr_3.4.3       reprex_0.3.0      digest_0.6.25    
## [85] webshot_0.5.2     munsell_0.5.0     viridisLite_0.3.0